This invention relates generally to the determination of turbine blade cross-sectional area, and more particularly to a method and apparatus for continuously determining the cross-sectional area of tapered twisted turbine blades along their lengths.
As is well known, the natural frequency of vibration in turbine blades and disks utilized in turbomachinery depends not only upon the size and shape of the particular blade or disk, but also upon its mode of vibration. Since this natural frequency of vibration may be typically on the order of 500 to 1000 Hertz, a number of reversals (i.e., fluctuating stress cycles) may be experienced thereby quickly reaching the fatigue limits of most conventional materials used in such turbomachinery. For example, it would not be unlikely to encounter 10.sup.6 fluctuating stress cycles per hour.
In conditions of extreme centripetal loading, such as in the operation of a conventional steam turbine, mechanical damping of the blades and disk assembly is most often provided by the material of the blades and disk assembly, as well as aerodynamic damping. Moreover, if a blade or disk assembly is excited at a frequency that closely approximates one of its fundamental natural frequencies, large amplitudes of vibration and, thus, high vibratory stress can result thereby leading to fatigue failure of the blade or disk assembly. Such excitations are desirably avoided since they can further lead to the requirement for expensive blade de-tuning in those cases where severe vibratory stresses are discovered during the manufacture of blade prototypes.
Prior to the introduction of "freestanding" turbine blades, turbine blades were typically attached one to the other at intermittent points along their lengths. As a result, the ranges of their natural frequencies of vibration did not pose much of a problem. However, with the advent of "freestanding" blades (i.e., blades which are not attached to adjacent blades except through the rotor attachment), concern for the vibratory characteristics of each individual blades has grown. Such concern is of particular importance in turbine blades of the tapered twisted configuration which have an extremely complex blade geometry, since the mass distribution along the length of such blades may affect the blade's basic strength and its ability to withstand stress induced by vibration, as well as its basic vibrational characteristics.
In order to minimize the problems associated with such vibration-induced stress, manufacturers in the past have paid strict attention to the quality control of blade sizing. One method currently in use by the assignee of the present invention is referred to generally as "pantoscribing", and consists of meticulously tracing around the airfoil profile of the blade at selected points along its length. This can be accomplished by rotating the blade about its centroidal axis, determining the area within a given airfoil profile at a plurality of selected points, plotting such determined areas relative to their positions along the blade length, and thereafter assuming that the area distribution between any given pair of points changes in a linear manner.
The above described method presents certain obvious problems. First, the method of tracing a blade airfoil is an extremely slow process. For example, in spite of the fact that only a few cross-sectional area data points must be obtained for any given blade, the tracing process of a single, average-size blade over its entire length can take several hours. As a result, only a very limited sample of a given production set of blades may be measured. Not only does such a process become time consuming, but it also increases the probability of manufacturing defective turbine blades due to the size of the statistically small sample group. Second, as was mentioned herein above with respect to the description of the pantoscribing method, an assumption is made that the area distribution between any given pair of points changes (i.e., decreases radially) in a linear manner. As is obviously the case, the chance that any manufactured blade has a cross-sectional area distribution which varies linearly is remote.